This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement invetvals (FIA re-measurment period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(G\) with increasing \(B\), thus, weighted nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {mean B_{t1}}\) in equal-sample sized plot biomass bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is used to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:
model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)
sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot-based filtering criteria:
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile thresholding approach. We also calculated plot \(G_{TI}\) using as summed tree incremental growth for all trees > 12.5 cm (5 inches) (see supplementary methods). We use the difference between the two methods, which we define \(diff_G\) as the difference between the two methods \(G_{MB} - G_{TI}\) to identify erroneous or outlier growth calculations. We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1760 observations.
Below the model fitting procedure is implemented by ecoprovince:
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6822 6736.7
## 2 6821 6721.5 1 15.195 15.42 8.693e-05 ***
## 3 6820 6431.3 1 290.282 307.83 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 27051.87
## 2 2 27038.46
## 3 3 26739.15
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.009888 0.165037 -0.060 0.952
## phi 0.019998 0.005047 3.963 7.49e-05 ***
## alpha 0.634061 0.033868 18.721 < 2e-16 ***
## A 3.581300 0.119640 29.934 < 2e-16 ***
## k 6.522308 0.615369 10.599 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9711 on 6820 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.129e-06
## (52 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6820 6431.3
## 2 6819 6422.8 1 8.4735 8.9962 0.002715 **
## 3 6819 6424.1 0 0.0000
## 4 6818 6422.7 1 1.3373 1.4196 0.233510
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 26739.15
## 2 3a 26732.16
## 3 3b 26733.53
## 4 3c 26734.11
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.010980 0.164841 -0.067 0.946895
## phi 0.020140 0.005047 3.991 6.66e-05 ***
## alpha 0.632787 0.033845 18.696 < 2e-16 ***
## A 3.649991 0.126777 28.791 < 2e-16 ***
## k 11.607027 2.534980 4.579 4.76e-06 ***
## p 0.243508 0.068055 3.578 0.000349 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9705 on 6819 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 2.248e-06
## (52 observations deleted due to missingness)
## Warning: Removed 17 rows containing missing values (geom_point).
## Warning: Removed 1038 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18911 20242
## 2 18906 20178 5 64.05 12.002 1.264e-11 ***
## 3 18905 19036 1 1142.81 1134.976 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70366.34
## 2 2 70297.09
## 3 3 69196.58
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.999943 0.163099 6.131 8.91e-10 ***
## phi 0.025881 0.003152 8.211 2.34e-16 ***
## alpha 0.806838 0.021956 36.748 < 2e-16 ***
## A 2.599578 0.070225 37.018 < 2e-16 ***
## k 10.057721 0.453530 22.177 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.003 on 18905 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.524e-06
## (3805 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18905 19036
## 2 18904 18862 1 173.649 174.037 < 2.2e-16 ***
## 3 18904 18877 0 0.000
## 4 18903 18860 1 17.168 17.208 3.365e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 69196.58
## 2 3a 69025.29
## 3 3b 69040.25
## 4 3c 69025.04
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.954318 0.159882 5.969 2.43e-09 ***
## phi 0.026434 0.003124 8.461 < 2e-16 ***
## alpha 0.799224 0.021796 36.669 < 2e-16 ***
## A 2.982149 0.151152 19.729 < 2e-16 ***
## k 25.323669 2.936663 8.623 < 2e-16 ***
## p 0.189430 0.033063 5.729 1.02e-08 ***
## s 0.840369 0.096756 8.685 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9989 on 18903 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.558e-06
## (3805 observations deleted due to missingness)
## Warning: Removed 1926 rows containing missing values (geom_point).
## Warning: Removed 1031 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7266 10676
## 2 7265 10653 1 22.84 15.577 7.997e-05 ***
## 3 7264 10214 1 438.37 311.752 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 32681.15
## 2 2 32667.58
## 3 3 32364.13
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.924852 0.125834 -7.350 2.2e-13 ***
## phi 0.019083 0.005448 3.503 0.000464 ***
## alpha 0.750989 0.039859 18.841 < 2e-16 ***
## A 5.243628 0.171545 30.567 < 2e-16 ***
## k 14.164894 1.593463 8.889 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.186 on 7264 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 9.323e-06
## (64 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7264 10214
## 2 7263 10127 1 86.861 62.294 3.393e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 32364.13
## 2 3a 32304.05
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.991815 0.121470 -8.165 3.76e-16 ***
## phi 0.020466 0.005431 3.768 0.000166 ***
## alpha 0.745886 0.039181 19.037 < 2e-16 ***
## A 7.709358 0.830328 9.285 < 2e-16 ***
## k 215.668276 75.532860 2.855 0.004312 **
## p 0.378545 0.029251 12.941 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.181 on 7263 degrees of freedom
##
## Number of iterations to convergence: 18
## Achieved convergence tolerance: 5.564e-06
## (64 observations deleted due to missingness)
## Warning: Removed 32 rows containing missing values (geom_point).
## Warning: Removed 1036 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4839 6092.2
## 2 4838 6083.5 1 8.735 6.9469 0.008423 **
## 3 4837 5798.3 1 285.221 237.9360 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 20152.37
## 2 2 20147.42
## 3 3 19916.91
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.165710 0.234835 -0.706 0.4804
## phi 0.021579 0.009282 2.325 0.0201 *
## alpha 0.774996 0.045980 16.855 <2e-16 ***
## A 4.302197 0.195800 21.972 <2e-16 ***
## k 18.366586 1.551671 11.837 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.095 on 4837 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.64e-06
## (1003 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4837 5798.3
## 2 4836 5686.0 1 112.22 95.442 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 19916.91
## 2 3a 19824.28
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.201434 0.229034 -0.879 0.3792
## phi 0.017214 0.009048 1.902 0.0572 .
## alpha 0.756562 0.045588 16.596 < 2e-16 ***
## A 6.225883 0.495601 12.562 < 2e-16 ***
## k 125.317993 25.375248 4.939 8.13e-07 ***
## p 0.250791 0.015405 16.280 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.084 on 4836 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 5.288e-06
## (1003 observations deleted due to missingness)
## Warning: Removed 489 rows containing missing values (geom_point).
## Warning: Removed 1053 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8742 11815
## 2 8741 11811 1 3.813 2.8219 0.09302 .
## 3 8740 11530 1 280.812 212.8594 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 36909.11
## 2 2 36908.29
## 3 3 36699.86
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.678595 0.137007 -4.953 7.44e-07 ***
## phi -0.012357 0.006662 -1.855 0.0637 .
## alpha 0.667559 0.042864 15.574 < 2e-16 ***
## A 4.813998 0.167516 28.738 < 2e-16 ***
## k 27.676460 2.451572 11.289 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.149 on 8740 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 7.363e-06
## (1265 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 3 36699.86
## 2 3a NA
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.678595 0.137007 -4.953 7.44e-07 ***
## phi -0.012357 0.006662 -1.855 0.0637 .
## alpha 0.667559 0.042864 15.574 < 2e-16 ***
## A 4.813998 0.167516 28.738 < 2e-16 ***
## k 27.676460 2.451572 11.289 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.149 on 8740 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 7.363e-06
## (1265 observations deleted due to missingness)
## Warning: Removed 620 rows containing missing values (geom_point).
## Warning: Removed 1002 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13233 32413
## 2 13232 32401 1 12.0 4.8986 0.0269 *
## 3 13231 29228 1 3172.8 1436.2611 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 69085.33
## 2 2 69082.43
## 3 3 67720.39
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.102065 0.172012 6.407 1.54e-10 ***
## phi 0.004936 0.004586 1.076 0.282
## alpha 0.868963 0.020677 42.026 < 2e-16 ***
## A 4.273767 0.121223 35.255 < 2e-16 ***
## k 1.136799 0.159419 7.131 1.05e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.486 on 13231 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.937e-06
## (281 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_231, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13231 29228
## 2 13230 29132 1 96.472 43.812 3.754e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 67720.39
## 2 3a 67678.63
## 3 3b 67680.30
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.048665 0.169018 6.204 5.65e-10 ***
## phi 0.005156 0.004571 1.128 0.259335
## alpha 0.868886 0.020547 42.288 < 2e-16 ***
## A 4.439114 0.131521 33.752 < 2e-16 ***
## k 7.625377 2.249531 3.390 0.000702 ***
## p 0.531025 0.050814 10.450 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.484 on 13230 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.12e-06
## (281 observations deleted due to missingness)
## Warning: Removed 143 rows containing missing values (geom_point).
## Warning: Removed 1017 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13303 36087
## 2 13302 36072 1 15.2 5.5979 0.018 *
## 3 13301 32458 1 3613.9 1480.9394 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 69162.02
## 2 2 69158.42
## 3 3 67755.75
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.779744 0.174483 4.469 7.93e-06 ***
## phi 0.005289 0.004831 1.095 0.274
## alpha 0.870086 0.020029 43.441 < 2e-16 ***
## A 4.431463 0.138940 31.895 < 2e-16 ***
## k 5.232230 0.410294 12.752 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.562 on 13301 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.162e-06
## (323 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13301 32458
## 2 13300 32149 1 308.467 127.611 < 2.2e-16 ***
## 3 13300 32173 0 0.000
## 4 13299 32149 1 24.192 10.008 0.001562 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 67755.75
## 2 3a 67630.69
## 3 3b 67640.55
## 4 3c 67632.54
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.699821 0.168755 4.147 3.39e-05 ***
## phi 0.004628 0.004787 0.967 0.334
## alpha 0.865348 0.019874 43.543 < 2e-16 ***
## A 4.879788 0.167465 29.139 < 2e-16 ***
## k 24.840494 3.992074 6.222 5.04e-10 ***
## p 0.399310 0.024277 16.448 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.555 on 13300 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 5.829e-06
## (323 observations deleted due to missingness)
## Warning: Removed 169 rows containing missing values (geom_point).
## Warning: Removed 931 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1324 3607.2
## 2 1323 3606.2 1 0.949 0.3483 0.5552
## 3 1322 3405.6 1 200.621 77.8782 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6965.867
## 2 2 6967.518
## 3 3 6893.561
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.90809 1.29228 1.477 0.1400
## phi -0.02371 0.02173 -1.091 0.2754
## alpha 0.80459 0.08194 9.820 < 2e-16 ***
## A 3.54620 0.68006 5.215 2.14e-07 ***
## k 4.45195 1.57213 2.832 0.0047 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.605 on 1322 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 6.242e-06
## (61 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 6893.561
## 2 3a NA
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.90809 1.29228 1.477 0.1400
## phi -0.02371 0.02173 -1.091 0.2754
## alpha 0.80459 0.08194 9.820 < 2e-16 ***
## A 3.54620 0.68006 5.215 2.14e-07 ***
## k 4.45195 1.57213 2.832 0.0047 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.605 on 1322 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 6.242e-06
## (61 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91821, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.7387, p-value = 0.000185
## alternative hypothesis: two.sided
## Warning: Removed 27 rows containing missing values (geom_point).
## Warning: Removed 645 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 77 126.36
## 2 76 126.07 1 0.2965 0.1787 0.67365
## 3 75 116.38 1 9.6919 6.2461 0.01463 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 417.9807
## 2 2 419.7928
## 3 3 415.3932
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.97364 1.75926 -0.553 0.58161
## phi 0.04865 0.06792 0.716 0.47601
## alpha 0.92741 0.33424 2.775 0.00697 **
## A 10.48547 4.92727 2.128 0.03662 *
## k 30.84036 15.66786 1.968 0.05272 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.246 on 75 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 8.084e-06
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 75 116.38
## 2 74 113.61 1 2.76491 1.8009 0.1837
## 3 74 113.44 0 0.00000
## 4 73 113.37 1 0.07089 0.0456 0.8314
## model AIC
## 1 3 415.3932
## 2 3a 415.4696
## 3 3b 415.3527
## 4 3c 417.3027
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.309e+00 1.485e+00 -0.882 0.38072
## phi 5.148e-02 6.724e-02 0.766 0.44632
## alpha 8.949e-01 3.344e-01 2.676 0.00917 **
## A 3.181e+01 1.075e+02 0.296 0.76811
## k 2.536e+03 4.364e+04 0.058 0.95382
## s 3.345e-01 3.981e-01 0.840 0.40345
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.238 on 74 degrees of freedom
##
## Number of iterations to convergence: 20
## Achieved convergence tolerance: 1.797e-06
## (3 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88149, p-value = 2.186e-06
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.1089, p-value = 0.2675
## alternative hypothesis: two.sided
## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 725 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1785 2717.6
## 2 1784 2714.0 1 3.6387 2.3919 0.122145
## 3 1783 2700.9 1 13.0325 8.6033 0.003398 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7661.536
## 2 2 7661.140
## 3 3 7654.534
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.16616 0.50732 0.328 0.74331
## phi 0.01898 0.01401 1.354 0.17578
## alpha 0.37133 0.12160 3.054 0.00229 **
## A 3.36013 0.32889 10.216 < 2e-16 ***
## k 15.64879 3.31387 4.722 2.52e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.231 on 1783 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 8.748e-06
## (507 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1783 2700.9
## 2 1781 2589.1 2 111.85 38.47 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 7654.534
## 2 3a NA
## 3 3b NA
## 4 3c 7582.913
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.13781 0.43699 -0.315 0.753
## phi 0.02415 0.01369 1.764 0.078 .
## alpha 0.18907 0.11545 1.638 0.102
## A 9.65502 15.02288 0.643 0.521
## k 326.59086 478.82390 0.682 0.495
## s 2.22000 1.13686 1.953 0.051 .
## p 0.24537 0.39035 0.629 0.530
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.206 on 1781 degrees of freedom
##
## Number of iterations to convergence: 20
## Achieved convergence tolerance: 8.752e-06
## (507 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.72987, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.7932, p-value = 1.097e-11
## alternative hypothesis: two.sided
## Warning: Removed 254 rows containing missing values (geom_point).
## Warning: Removed 1176 row(s) containing missing values (geom_path).
## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
note: model fit, but fit was funky due to data being sparse
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 212 109.50
## 2 211 107.99 1 1.5070 2.9444 0.08765 .
## 3 210 103.86 1 4.1364 8.3639 0.00423 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 506.5831
## 2 2 505.6036
## 3 3 499.2067
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.60390 0.75643 -2.120 0.03515 *
## phi -0.09495 0.07250 -1.310 0.19176
## alpha 0.82023 0.25228 3.251 0.00134 **
## A 4.22990 1.38936 3.044 0.00263 **
## k 124.24892 42.33717 2.935 0.00371 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7032 on 210 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 1.944e-06
## (3 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_313, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 210 103.856
## 2 209 101.102 1 2.7533 5.6916 0.01794 *
## 3 208 98.863 1 2.2389 4.7105 0.03111 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 499.2067
## 2 3a 495.4300
## 3 3b NA
## 4 3c 492.6153
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.59741 0.73738 -2.166 0.031422 *
## phi -0.08343 0.06684 -1.248 0.213356
## alpha 0.83684 0.24358 3.436 0.000714 ***
## A 3.16355 1.01981 3.102 0.002188 **
## k 111.46478 26.09832 4.271 2.96e-05 ***
## s 2.87973 1.34426 2.142 0.033336 *
## p 0.30573 0.09555 3.200 0.001591 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6894 on 208 degrees of freedom
##
## Number of iterations to convergence: 20
## Achieved convergence tolerance: 8.622e-06
## (3 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97899, p-value = 0.002688
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.36661, p-value = 0.7139
## alternative hypothesis: two.sided
## Warning: Removed 1103 row(s) containing missing values (geom_path).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_331, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 193 173.52
## 2 192 173.47 1 0.0524 0.0579 0.81003
## 3 191 168.50 1 4.9689 5.6324 0.01862 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 665.6359
## 2 2 667.5768
## 3 3 663.8805
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.51605 1.63140 0.316 0.75210
## phi 0.01497 0.03142 0.477 0.63424
## alpha 0.66415 0.25423 2.612 0.00971 **
## A 3.91042 1.26582 3.089 0.00231 **
## k 57.76819 18.99786 3.041 0.00269 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9393 on 191 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.985e-06
## (36 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 191 168.50
## 2 190 160.32 1 8.1820 9.6969 0.002131 **
## 3 189 158.12 1 2.1996 2.6292 0.106584
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 663.8805
## 2 3a 656.1243
## 3 3b NA
## 4 3c 655.4165
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.17215 1.38113 0.125 0.90094
## phi 0.02067 0.03102 0.666 0.50596
## alpha 0.68028 0.22567 3.014 0.00293 **
## A 3.79683 1.23637 3.071 0.00245 **
## k 84.69132 26.33183 3.216 0.00153 **
## p 0.29323 0.09705 3.021 0.00286 **
## s 2.36410 1.17963 2.004 0.04649 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9147 on 189 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 7.581e-06
## (36 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91018, p-value = 1.565e-09
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.4234, p-value = 0.1546
## alternative hypothesis: two.sided
## Warning: Removed 18 rows containing missing values (geom_point).
## Warning: Removed 1120 row(s) containing missing values (geom_path).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 112 82.270
## 2 111 82.264 1 0.0062 0.0083 0.927546
## 3 110 74.204 1 8.0592 11.9469 0.000779 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 315.0331
## 2 2 317.0245
## 3 3 307.1674
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.96617 5.50627 0.357 0.721718
## phi 0.00124 0.05446 0.023 0.981879
## alpha 0.98497 0.24440 4.030 0.000103 ***
## A 3.26566 2.69600 1.211 0.228376
## k 82.57910 32.74227 2.522 0.013097 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8213 on 110 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.047e-06
## (9 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 110 74.204
## 2 109 74.164 1 0.040526 0.0596 0.8076
## 3 109 74.195 0 0.000000
## 4 108 74.158 1 0.036489 0.0531 0.8181
## model AIC
## 1 3 307.1674
## 2 3a 309.1046
## 3 3b 309.1521
## 4 3c 311.0955
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.96617 5.50627 0.357 0.721718
## phi 0.00124 0.05446 0.023 0.981879
## alpha 0.98497 0.24440 4.030 0.000103 ***
## A 3.26566 2.69600 1.211 0.228376
## k 82.57910 32.74227 2.522 0.013097 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8213 on 110 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.047e-06
## (9 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9487, p-value = 0.0002425
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.94042, p-value = 0.347
## alternative hypothesis: two.sided
## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1241 row(s) containing missing values (geom_path).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6746 5753.1
## 2 6745 5726.7 1 26.40 31.097 2.55e-08 ***
## 3 6744 5393.0 1 333.75 417.356 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25694.00
## 2 2 25664.96
## 3 3 25261.71
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.624232 0.198138 3.150 0.00164 **
## phi 0.019924 0.004531 4.397 1.11e-05 ***
## alpha 0.637587 0.029038 21.957 < 2e-16 ***
## A 2.999615 0.114078 26.294 < 2e-16 ***
## k 2.752660 0.406438 6.773 1.37e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8942 on 6744 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.222e-06
## (23 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6744 5393.0
## 2 6743 5389.8 1 3.1997 4.0030 0.045458 *
## 3 6743 5392.8 0 0.0000
## 4 6742 5385.3 1 7.5612 9.4662 0.002101 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 25261.71
## 2 3a 25259.70
## 3 3b 25263.50
## 4 3c 25256.03
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.60999 0.19692 3.098 0.00196 **
## phi 0.02012 0.00453 4.441 9.12e-06 ***
## alpha 0.63490 0.02899 21.901 < 2e-16 ***
## A 2.95554 0.11274 26.216 < 2e-16 ***
## k 9.93538 2.30225 4.316 1.62e-05 ***
## p 0.46592 0.07809 5.966 2.55e-09 ***
## s 1.85621 0.46313 4.008 6.19e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8937 on 6742 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 7.419e-06
## (23 observations deleted due to missingness)
## Warning: Removed 14 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8257 16789
## 2 8256 16786 1 2.46 1.2104 0.2713
## 3 8255 16418 1 368.11 185.0856 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 40113.33
## 2 2 40114.12
## 3 3 39932.96
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.020544 0.177726 0.116 0.908
## phi -0.004884 0.006639 -0.736 0.462
## alpha 0.814722 0.056701 14.369 < 2e-16 ***
## A 4.180968 0.157264 26.586 < 2e-16 ***
## k 7.281964 1.424676 5.111 3.27e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.41 on 8255 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 4.273e-06
## (55 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 39932.96
## 2 3a NA
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.020544 0.177726 0.116 0.908
## phi -0.004884 0.006639 -0.736 0.462
## alpha 0.814722 0.056701 14.369 < 2e-16 ***
## A 4.180968 0.157264 26.586 < 2e-16 ***
## k 7.281964 1.424676 5.111 3.27e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.41 on 8255 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 4.273e-06
## (55 observations deleted due to missingness)
## Warning: Removed 27 rows containing missing values (geom_point).
## Warning: Removed 982 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 887 1339.4
## 2 886 1339.3 1 0.140 0.0923 0.7613
## 3 885 1292.8 1 46.501 31.8328 2.261e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3727.581
## 2 2 3729.488
## 3 3 3700.038
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.61273 1.92481 1.877 0.0609 .
## phi -0.01887 0.02481 -0.761 0.4471
## alpha 0.92667 0.15103 6.136 1.28e-09 ***
## A 1.67614 0.38072 4.402 1.20e-05 ***
## k 3.83833 3.27829 1.171 0.2420
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.209 on 885 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 4.701e-06
## (6 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 3700.038
## 2 3a NA
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.61273 1.92481 1.877 0.0609 .
## phi -0.01887 0.02481 -0.761 0.4471
## alpha 0.92667 0.15103 6.136 1.28e-09 ***
## A 1.67614 0.38072 4.402 1.20e-05 ***
## k 3.83833 3.27829 1.171 0.2420
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.209 on 885 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 4.701e-06
## (6 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94516, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.1788, p-value = 0.02935
## alternative hypothesis: two.sided
## Warning: Removed 6 rows containing missing values (geom_point).
## Warning: Removed 1175 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 989 1487.8
## 2 988 1466.1 1 21.624 14.572 0.0001433 ***
## 3 987 1403.8 1 62.340 43.831 5.869e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4215.211
## 2 2 4202.687
## 3 3 4161.584
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.64775 1.69266 1.564 0.11808
## phi 0.07074 0.02643 2.677 0.00756 **
## alpha 0.76844 0.10741 7.154 1.64e-12 ***
## A 1.83534 0.41750 4.396 1.22e-05 ***
## k 1.60048 0.96067 1.666 0.09603 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.193 on 987 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 7.134e-06
## (14 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 4161.584
## 2 3a NA
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.64775 1.69266 1.564 0.11808
## phi 0.07074 0.02643 2.677 0.00756 **
## alpha 0.76844 0.10741 7.154 1.64e-12 ***
## A 1.83534 0.41750 4.396 1.22e-05 ***
## k 1.60048 0.96067 1.666 0.09603 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.193 on 987 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 7.134e-06
## (14 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95429, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.4242, p-value = 5.823e-08
## alternative hypothesis: two.sided
## Warning: Removed 7 rows containing missing values (geom_point).
## Warning: Removed 1218 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3147 8417.1
## 2 3146 8404.1 1 12.96 4.8528 0.02767 *
## 3 3145 8007.1 1 397.02 155.9417 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 16149.88
## 2 2 16147.03
## 3 3 15996.59
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.64015 0.24959 -6.571 5.81e-11 ***
## phi -0.02633 0.01749 -1.505 0.132
## alpha 0.96541 0.06969 13.854 < 2e-16 ***
## A 12.37097 1.06955 11.567 < 2e-16 ***
## k 128.53784 10.22671 12.569 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.596 on 3145 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.151e-06
## (74 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3145 8007.1
## 2 3144 7892.5 1 114.589 45.647 1.681e-11 ***
## 3 3144 7925.1 0 0.000
## 4 3143 7880.2 1 44.853 17.889 2.408e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 15996.59
## 2 3a 15953.18
## 3 3b 15966.16
## 4 3c 15950.28
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.63573 0.24760 -6.606 4.61e-11 ***
## phi -0.02333 0.01726 -1.352 0.176
## alpha 0.93860 0.07003 13.403 < 2e-16 ***
## A 11.22362 1.11339 10.081 < 2e-16 ***
## k 166.50196 18.41444 9.042 < 2e-16 ***
## p 0.20777 0.02940 7.068 1.93e-12 ***
## s 1.65252 0.23988 6.889 6.76e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.583 on 3143 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 8.027e-06
## (74 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92449, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.9781, p-value = 6.423e-07
## alternative hypothesis: two.sided
## Warning: Removed 39 rows containing missing values (geom_point).
## Warning: Removed 126 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1682 3723.6
## 2 1681 3593.1 1 130.459 61.034 9.807e-15 ***
## 3 1680 3507.6 1 85.504 40.953 2.017e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7999.216
## 2 2 7941.121
## 3 3 7902.539
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.55370 0.36681 -4.236 2.40e-05 ***
## phi 0.16330 0.01741 9.382 < 2e-16 ***
## alpha 0.72152 0.10445 6.908 6.95e-12 ***
## A 15.71695 1.85052 8.493 < 2e-16 ***
## k 183.91121 21.84212 8.420 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.445 on 1680 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.978e-06
## (292 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1680 3507.6
## 2 1679 3472.9 1 34.721 16.786 4.383e-05 ***
## 3 1679 3492.3 0 0.000
## 4 1678 3469.0 1 23.332 11.286 0.0007985 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 7902.539
## 2 3a 7887.776
## 3 3b 7897.190
## 4 3c 7887.895
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.57373 0.35934 -4.380 1.26e-05 ***
## phi 0.16399 0.01724 9.511 < 2e-16 ***
## alpha 0.70751 0.10290 6.876 8.66e-12 ***
## A 19.41660 2.88667 6.726 2.38e-11 ***
## k 340.27521 77.07101 4.415 1.07e-05 ***
## p 0.06498 0.01245 5.221 2.00e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.438 on 1679 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 2.647e-06
## (292 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89406, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.082746, p-value = 0.9341
## alternative hypothesis: two.sided
## Warning: Removed 155 rows containing missing values (geom_point).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 363 173.85
## 2 362 167.67 1 6.1874 13.359 0.0002952 ***
## 3 361 151.94 1 15.7225 37.355 2.554e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 867.4285
## 2 2 856.1651
## 3 3 822.1268
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.06635 0.35148 -5.879 9.40e-09 ***
## phi 0.06118 0.02220 2.757 0.00614 **
## alpha 0.78833 0.11296 6.979 1.43e-11 ***
## A 10.63664 2.05685 5.171 3.86e-07 ***
## k 160.22129 38.00285 4.216 3.15e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6488 on 361 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.837e-06
## (1 observation deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M313, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 361 151.94
## 2 360 151.06 1 0.88856 2.1176 0.1465
## model AIC
## 1 3 822.1268
## 2 3a 821.9802
## 3 3b 821.6317
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.057e+00 3.537e-01 -5.815 1.34e-08 ***
## phi 6.070e-02 2.224e-02 2.729 0.006668 **
## alpha 7.848e-01 1.131e-01 6.942 1.81e-11 ***
## A 5.415e+01 1.907e+02 0.284 0.776569
## k 3.935e+03 2.527e+04 0.156 0.876316
## s 6.923e-01 1.775e-01 3.900 0.000115 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6475 on 360 degrees of freedom
##
## Number of iterations to convergence: 22
## Achieved convergence tolerance: 8.299e-07
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97137, p-value = 1.275e-06
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.47103, p-value = 0.6376
## alternative hypothesis: two.sided
## Warning: Removed 1183 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1732 1567.7
## 2 1731 1548.6 1 19.07 21.316 4.182e-06 ***
## 3 1730 1445.7 1 102.91 123.143 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4946.994
## 2 2 4927.760
## 3 3 4810.458
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.48851 0.66592 -0.734 0.463
## phi 0.09081 0.01449 6.266 4.68e-10 ***
## alpha 0.72031 0.05452 13.212 < 2e-16 ***
## A 2.58293 0.43178 5.982 2.67e-09 ***
## k 37.69903 6.08368 6.197 7.19e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9141 on 1730 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.369e-06
## (21 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1730 1445.7
## 2 1729 1415.8 1 29.836 36.435 1.927e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 4810.458
## 2 3a 4776.276
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.22164 0.74109 -0.299 0.7649
## phi 0.09382 0.01430 6.562 7.01e-11 ***
## alpha 0.73135 0.05290 13.824 < 2e-16 ***
## A 7.18085 4.09409 1.754 0.0796 .
## k 612.34714 500.06592 1.225 0.2209
## p 0.11073 0.05384 2.057 0.0399 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9049 on 1729 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 1.434e-06
## (21 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.8548, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.414, p-value = 1.015e-05
## alternative hypothesis: two.sided
## Warning: Removed 7 rows containing missing values (geom_point).
## Warning: Removed 1091 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2513 2864.1
## 2 2512 2859.8 1 4.302 3.7787 0.05202 .
## 3 2511 2603.5 1 256.310 247.2055 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8728.807
## 2 2 8727.025
## 3 3 8492.774
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.91771 0.42327 -2.168 0.0302 *
## phi 0.02631 0.01737 1.515 0.1300
## alpha 0.90510 0.04945 18.302 < 2e-16 ***
## A 4.94379 0.62849 7.866 5.39e-15 ***
## k 64.39021 7.07215 9.105 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.018 on 2511 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 9.236e-06
## (96 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2511 2603.5
## 2 2510 2491.6 1 111.878 112.7038 <2e-16 ***
## 3 2509 2491.2 1 0.432 0.4356 0.5093
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 8492.774
## 2 3a 8384.264
## 3 3b NA
## 4 3c 8385.827
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.96761 0.39955 -2.422 0.01552 *
## phi 0.02091 0.01696 1.233 0.21760
## alpha 0.88857 0.04853 18.310 < 2e-16 ***
## A 15.40333 5.95451 2.587 0.00974 **
## k 760.03188 384.19799 1.978 0.04801 *
## p 0.07577 0.02482 3.053 0.00229 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9963 on 2510 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.075e-06
## (96 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90479, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -7.0048, p-value = 2.473e-12
## alternative hypothesis: two.sided
## Warning: Removed 46 rows containing missing values (geom_point).
## Warning: Removed 1001 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1691 2122.4
## 2 1690 2120.4 1 2.008 1.6001 0.2061
## 3 1689 1851.2 1 269.153 245.5647 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6712.211
## 2 2 6712.608
## 3 3 6484.655
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.58199 0.57724 -1.008 0.313
## phi 0.00104 0.01880 0.055 0.956
## alpha 0.94886 0.05266 18.017 < 2e-16 ***
## A 5.54606 0.82458 6.726 2.38e-11 ***
## k 44.21369 4.89817 9.027 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.047 on 1689 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.004e-06
## (59 observations deleted due to missingness)
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1689 1851.2
## 2 1688 1754.0 1 97.241 93.582 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 6484.655
## 2 3a 6395.251
## 3 3b NA
## 4 3c NA
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 -
## p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.670171 0.536892 -1.248 0.212115
## phi 0.006873 0.018253 0.377 0.706553
## alpha 0.930227 0.050682 18.354 < 2e-16 ***
## A 13.343494 3.465477 3.850 0.000122 ***
## k 466.537719 163.579207 2.852 0.004397 **
## p 0.114498 0.020826 5.498 4.43e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.019 on 1688 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 2.994e-06
## (59 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93155, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.6597, p-value = 3.167e-06
## alternative hypothesis: two.sided
## Warning: Removed 29 rows containing missing values (geom_point).
## Warning: Removed 925 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 355 353.04
## 2 354 353.04 1 0.0053 0.0053 0.9422
## 3 353 326.43 1 26.6098 28.7760 1.473e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1090.416
## 2 2 1092.410
## 3 3 1066.355
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.13825 3.71884 0.575 0.56567
## phi -0.03467 0.03674 -0.944 0.34601
## alpha 0.81562 0.13184 6.186 1.7e-09 ***
## A 1.66966 0.86432 1.932 0.05419 .
## k 29.26846 9.25921 3.161 0.00171 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9616 on 353 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.954e-06
## (101 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 353 326.43
## 2 352 326.35 1 0.07658 0.0826 0.7740
## 3 352 326.42 0 0.00000
## 4 351 325.72 1 0.69849 0.7527 0.3862
## model AIC
## 1 3 1066.355
## 2 3a 1068.271
## 3 3b 1068.347
## 4 3c 1069.580
##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.13825 3.71884 0.575 0.56567
## phi -0.03467 0.03674 -0.944 0.34601
## alpha 0.81562 0.13184 6.186 1.7e-09 ***
## A 1.66966 0.86432 1.932 0.05419 .
## k 29.26846 9.25921 3.161 0.00171 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9616 on 353 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.954e-06
## (101 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.83081, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.3928, p-value = 0.01672
## alternative hypothesis: two.sided
## Warning: Removed 48 rows containing missing values (geom_point).
## Warning: Removed 1264 row(s) containing missing values (geom_path).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3a |
| 212 | Laurentian Mixed Forest | 3c |
| 221 | Eastern Broadleaf Forest | 3a |
| 222 | Midwest Broadleaf Forest | 3a |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3a |
| 232 | Outer Coastal Plain Mixed Forest | 3a |
| 234 | Lower Mississippi Riverine Forest | 3 |
| 242 | Pacific Lowland Mixed Forest | 3b |
| 251 | Prairie Parkland (Temperate) | 3c |
| 255 | Prairie Parkland (Subtropical) | NA |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | 3c |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | 3c |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | 3 |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3c |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3 |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | 3 |
| M242 | Cascade Mixed Forest | 3c |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3a |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 3b |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 3a |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3a |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3a |
| M334 | Black Hills Coniferous Forest | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.variance | ge.2.5 | ge.97.5 | phi | phi.variance | phi.2.5 | phi.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6877 | 2876 | -0.0109798 | 0.0271725 | -0.3341190 | 0.3121593 | 0.0201397 | 0.0000255 | 0.0102465 | 0.0300329 | 0.6327874 | 0.0011455 | 0.5664398 | 0.6991349 | 3.649991 | 3.4014689 | 3.898513 | 11.607027 | 6.637676e+00 | 16.576378 |
| 212 | Laurentian Mixed Forest | east | 22715 | 9499 | 0.9543179 | 0.0255622 | 0.6409350 | 1.2677008 | 0.0264340 | 0.0000098 | 0.0203104 | 0.0325575 | 0.7992242 | 0.0004750 | 0.7565030 | 0.8419454 | 2.982149 | 2.6858766 | 3.278421 | 25.323669 | 1.956755e+01 | 31.079791 |
| 221 | Eastern Broadleaf Forest | east | 7333 | 3571 | -0.9918148 | 0.0147550 | -1.2299315 | -0.7536982 | 0.0204655 | 0.0000295 | 0.0098185 | 0.0311126 | 0.7458855 | 0.0015351 | 0.6690800 | 0.8226910 | 7.709358 | 6.0816742 | 9.337041 | 215.668276 | 6.760192e+01 | 363.734636 |
| 222 | Midwest Broadleaf Forest | east | 5845 | 2589 | -0.2014342 | 0.0524564 | -0.6504441 | 0.2475757 | 0.0172135 | 0.0000819 | -0.0005251 | 0.0349522 | 0.7565621 | 0.0020782 | 0.6671896 | 0.8459346 | 6.225883 | 5.2542798 | 7.197486 | 125.317993 | 7.557097e+01 | 175.065015 |
| 223 | Central Interior Broadleaf Forest | east | 10010 | 3864 | -0.6785951 | 0.0187709 | -0.9471607 | -0.4100296 | -0.0123567 | 0.0000444 | -0.0254161 | 0.0007028 | 0.6675588 | 0.0018373 | 0.5835355 | 0.7515820 | 4.813998 | 4.4856269 | 5.142368 | 27.676460 | 2.287080e+01 | 32.482119 |
| 231 | Southeastern Mixed Forest | east | 13517 | 6193 | 1.0486648 | 0.0285670 | 0.7173659 | 1.3799636 | 0.0051558 | 0.0000209 | -0.0038035 | 0.0141151 | 0.8688863 | 0.0004222 | 0.8286110 | 0.9091615 | 4.439114 | 4.1813147 | 4.696913 | 7.625377 | 3.215974e+00 | 12.034780 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13629 | 6626 | 0.6998205 | 0.0284781 | 0.3690375 | 1.0306036 | 0.0046285 | 0.0000229 | -0.0047556 | 0.0140125 | 0.8653484 | 0.0003950 | 0.8263934 | 0.9043033 | 4.879788 | 4.5515323 | 5.208044 | 24.840494 | 1.701546e+01 | 32.665527 |
| 234 | Lower Mississippi Riverine Forest | east | 1388 | 778 | 1.9080853 | 1.6699841 | -0.6270554 | 4.4432259 | -0.0237106 | 0.0004721 | -0.0663363 | 0.0189152 | 0.8045919 | 0.0067133 | 0.6438550 | 0.9653287 | 3.546196 | 2.2120751 | 4.880317 | 4.451952 | 1.367813e+00 | 7.536091 |
| 242 | Pacific Lowland Mixed Forest | pacific | 83 | 83 | -1.3094645 | 2.2049734 | -4.2682228 | 1.6492938 | 0.0514806 | 0.0045209 | -0.0824926 | 0.1854538 | 0.8948735 | 0.1118244 | 0.2285640 | 1.5611830 | 31.807945 | -182.3604934 | 245.976384 | 2535.570834 | -8.442068e+04 | 89491.824379 |
| 251 | Prairie Parkland (Temperate) | east | 2295 | 906 | -0.1378060 | 0.1909590 | -0.9948703 | 0.7192584 | 0.0241500 | 0.0001875 | -0.0027081 | 0.0510081 | 0.1890667 | 0.0133288 | -0.0373654 | 0.4154989 | 9.655022 | -19.8093113 | 39.119354 | 326.590858 | -6.125250e+02 | 1265.706671 |
| 255 | Prairie Parkland (Subtropical) | east | 717 | 319 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 25 | 25 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 163 | 161 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 218 | 218 | -1.5974077 | 0.5437229 | -3.0510957 | -0.1437198 | -0.0834260 | 0.0044671 | -0.2151894 | 0.0483374 | 0.8368358 | 0.0593329 | 0.3566271 | 1.3170445 | 3.163546 | 1.1530601 | 5.174031 | 111.464778 | 6.001365e+01 | 162.915911 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 331 | 255 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 232 | 128 | 0.1721477 | 1.9075230 | -2.5522646 | 2.8965600 | 0.0206740 | 0.0009624 | -0.0405219 | 0.0818700 | 0.6802818 | 0.0509272 | 0.2351253 | 1.1254384 | 3.796826 | 1.3579755 | 6.235677 | 84.691316 | 3.274928e+01 | 136.633353 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 124 | 123 | 1.9661658 | 30.3190383 | -8.9459742 | 12.8783057 | 0.0012399 | 0.0029665 | -0.1066972 | 0.1091770 | 0.9849740 | 0.0597331 | 0.5006233 | 1.4693246 | 3.265664 | -2.0771713 | 8.608500 | 82.579097 | 1.769160e+01 | 147.466598 |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6772 | 3006 | 0.6099912 | 0.0387780 | 0.2239634 | 0.9960191 | 0.0201180 | 0.0000205 | 0.0112368 | 0.0289992 | 0.6348976 | 0.0008404 | 0.5780693 | 0.6917259 | 2.955542 | 2.7345424 | 3.176542 | 9.935383 | 5.422256e+00 | 14.448511 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8315 | 3810 | 0.0205444 | 0.0315866 | -0.3278434 | 0.3689322 | -0.0048836 | 0.0000441 | -0.0178978 | 0.0081307 | 0.8147216 | 0.0032150 | 0.7035727 | 0.9258705 | 4.180968 | 3.8726905 | 4.489246 | 7.281964 | 4.489240e+00 | 10.074688 |
| M223 | Ozark Broadleaf Forest Meadow | east | 896 | 349 | 3.6127264 | 3.7049024 | -0.1650029 | 7.3904556 | -0.0188729 | 0.0006156 | -0.0675679 | 0.0298222 | 0.9266739 | 0.0228087 | 0.6302641 | 1.2230837 | 1.676141 | 0.9289120 | 2.423370 | 3.838332 | -2.595798e+00 | 10.272462 |
| M231 | Ouachita Mixed Forest | east | 1006 | 495 | 2.6477547 | 2.8650948 | -0.6738694 | 5.9693788 | 0.0707385 | 0.0006985 | 0.0188744 | 0.1226026 | 0.7684380 | 0.0115370 | 0.5576591 | 0.9792169 | 1.835343 | 1.0160634 | 2.654623 | 1.600476 | -2.847238e-01 | 3.485676 |
| M242 | Cascade Mixed Forest | pacific | 3224 | 3207 | -1.6357285 | 0.0613078 | -2.1212104 | -1.1502465 | -0.0233320 | 0.0002978 | -0.0571692 | 0.0105052 | 0.9385960 | 0.0049041 | 0.8012878 | 1.0759041 | 11.223621 | 9.0405696 | 13.406671 | 166.501965 | 1.303964e+02 | 202.607509 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1977 | 1807 | -1.5737277 | 0.1291222 | -2.2785210 | -0.8689343 | 0.1639934 | 0.0002973 | 0.1301737 | 0.1978132 | 0.7075065 | 0.0105879 | 0.5056853 | 0.9093277 | 19.416604 | 13.7547440 | 25.078464 | 340.275212 | 1.891098e+02 | 491.440588 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 367 | 367 | -2.0566556 | 0.1250833 | -2.7521765 | -1.3611346 | 0.0606986 | 0.0004948 | 0.0169552 | 0.1044421 | 0.7848411 | 0.0127830 | 0.5624961 | 1.0071860 | 54.151313 | -320.8143982 | 429.117024 | 3935.373875 | -4.575415e+04 | 53624.896968 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1756 | 1756 | -0.2216358 | 0.5492199 | -1.6751703 | 1.2318986 | 0.0938226 | 0.0002045 | 0.0657782 | 0.1218671 | 0.7313497 | 0.0027987 | 0.6275896 | 0.8351097 | 7.180848 | -0.8490325 | 15.210729 | 612.347135 | -3.684506e+02 | 1593.144911 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2612 | 2602 | -0.9676071 | 0.1596412 | -1.7510910 | -0.1841233 | 0.0209145 | 0.0002876 | -0.0123404 | 0.0541694 | 0.8885691 | 0.0023551 | 0.7934078 | 0.9837304 | 15.403326 | 3.7270718 | 27.079581 | 760.031876 | 6.654360e+00 | 1513.409391 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1753 | 1742 | -0.6701713 | 0.2882529 | -1.7232151 | 0.3828726 | 0.0068732 | 0.0003332 | -0.0289277 | 0.0426742 | 0.9302266 | 0.0025687 | 0.8308201 | 1.0296332 | 13.343494 | 6.5464106 | 20.140578 | 466.537719 | 1.456983e+02 | 787.377126 |
| M334 | Black Hills Coniferous Forest | interior west | 459 | 181 | 2.1382508 | 13.8297772 | -5.1756196 | 9.4521211 | -0.0346717 | 0.0013501 | -0.1069349 | 0.0375915 | 0.8156215 | 0.0173818 | 0.5563309 | 1.0749121 | 1.669664 | -0.0302026 | 3.369531 | 29.268462 | 1.105831e+01 | 47.478618 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 220 | 220 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning: Removed 14 rows containing missing values (geom_point).
## Warning: Removed 14 rows containing missing values (geom_point).
## region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1 entire US 0.11390352 0.06580423 0.242879814 -0.01507276
## 2 pacific -0.14153116 0.01783556 -0.106573459 -0.17648887
## 3 east 0.33357842 0.05129085 0.434108486 0.23304835
## 4 interior west -0.07814373 0.03716635 -0.005297675 -0.15098978
## region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1 entire US 0.016793959 0.002045228 0.020802607
## 2 pacific 0.003897856 0.001100690 0.006055209
## 3 east 0.008895102 0.001336975 0.011515572
## 4 interior west 0.004001002 0.001088090 0.006133657
## 95 % CI, lower
## 1 0.012785312
## 2 0.001740503
## 3 0.006274631
## 4 0.001868346
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.77078681 0.010164810 0.79070984
## 2 pacific 0.07531836 0.005056256 0.08522862
## 3 east 0.59114245 0.008128291 0.60707390
## 4 interior west 0.10432600 0.003418849 0.11102695
## 95 % CI, lower
## 1 0.75086378
## 2 0.06540810
## 3 0.57521100
## 4 0.09762506
## region weighted.A
## 1 entire US 6.389644
## 2 pacific 13.954195
## 3 east 4.421361
## 4 interior west 12.689849
## region weighted.k
## 1 entire US 151.33635
## 2 pacific 257.29727
## 3 east 45.53192
## 4 interior west 696.34581